An analytic expression is derived for the Lyapunov exponents of the product of random transfer matrices related to the Ising model with quenched disorder in one dimension. We find a deterministic map which transforms the original system into a new one with zero external field and constant coupling. The free energy and the rate of correlation decay are thus obtained in terms of an exponentially convergent series. Our results can be generalized to the product of random matrices with nonzero entries.
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